We considered the non-local operator consisting of two gluon field strength
tensors connected by a straight Wilson line and studied its VEV, which is
determined by two nonperturbative Lorentz scalar functions.
For each of the latter, we performed an OPE through mass dimension four, which,
besides a purely perturbative structure function, involves the VEVs of three
local operators, and calculated the AD of the structure function and the CFs of
the three local operators through three loops, order \(a^3\) , in the modified
minimal-subtraction (\(\overline{\mathrm {MS}}\) ) scheme.
In our recent work [1]}, the structure functions were derived
through three loops and the ADs through two loops.
Using the ADs, we also performed a RG improvement of the structure functions
and presented their renormalization scheme invariant counterparts thus
resulting, again through three loops.
These results should be of interest to the lattice QCD community in studies of
the QCD vacuum structure and serve as normalization factors in
calculations of gluon PDFs within the qPDF approach, eliminating the need for
nonperturbative subtractions of linear divergences.
